Not a polish nut at all LOL. I am not in either camp. Clean and polish, or Leave as found. I take each new medal on its own merits in regards to my decision to clean or leave alone.
Basically if the medals are mounted as worn and the patina is pretty much even, I will clean up only if necessary with the soapy water. If the patina on the medal is uneven, it gets removed. If the medal is like this latest one, it will get cleaned and polished ONCE. My reasoning behind this, although likely flawed, is that in this case, the man it was issued to never wore it, never saw it.
This newest medal, I will clean and likely end up polishing due to the fact that black/dark stuff that can be seen in the photos, is sort of a gummy substance. What exactly it is, I do not know. I do know that it has to go.
Like you Lorne, I will use mild grease cutting dish soap (I use Dawn as it is what we use here at home for dishes) I will use warm water and a Q tip or cotton ball at first to see how it lifts off. I do not like to use a toothbrush as I am always afraid I may end up scratching the medal and leaving swirls in the medal.
I will use a silver dip for some medals as well. See my Colonial Auxiliary Forces Officers Decoration posted Here https://www.cdnmilitarycollectors.com/t2759-well-now-that-i-have-vd-i-am-looking-for-a-butt-nut
I am leery of the dip as well because I find it leaves sort of a frosted look to the medal. I will also use my mothers old 'Silver Mitt" It is a very old one but is very very soft. I figure if she used it for 30 odd years to polish the silver tea serving set, I can use it on a medal once without harm.
I will not use a brillo or scrubbing pad, toothpaste and toothbrush, silvo, 0000 steel wool, or anything else. You may find it silly to say that, but I have seen and heard many times of people using these items to clean medals.
Of course I have always had trouble with Stars and bronze, brass medals as they are coated. I just use the soapy water.